Problem 12 · Maria and the clock change
The 18 saved minutes are 9 each way: they meet at 8:51.
Integer answer, at most 4 digitsThere is only one road from Lluís's house to Maria's. Every morning Lluís drives from his house to pick Maria up and bring her to his house. When he arrives at Maria's house, punctually at 9 a.m. every day, she is always ready and he picks her up and drives home. On the morning of 27 October, Maria forgot that the clocks had gone back from summer to winter time the night before. At 8 a.m., thinking it was 9, she waited at the front door and, not seeing Lluís, started walking along the road to meet his car. After a while she met the car coming to fetch her: Lluís stopped, picked Maria up, and the two of them arrived at Lluís's house 18 minutes earlier than usual. Lluís drove at constant speed and lost no time turning around and picking Maria up. How many minutes did Maria walk?
Reasoned solution
Key idea: the car's saving is the stretch it didn't have to drive — and it skips it twice: out and back.
Lluís leaves at his usual time and arrives $18$ minutes early: he saved $18$ minutes of driving. Since the stretch between the meeting point and Maria's house is skipped twice (out and back), that stretch is worth $9$ minutes by car.
So Lluís meets Maria at the point he normally passes $9$ minutes before $9$ a.m.: they meet at $8\!:\!51$.